We present a differentiable rendering framework to learn structured 3D abstractions in the form of primitive assemblies from sparse RGB images capturing a 3D object. By leveraging differentiable volume rendering, our method does not require 3D supervision. Architecturally, our network follows the general pipeline of an image-conditioned neural radiance field (NeRF) exemplified by pixelNeRF for color prediction. As our core contribution, we introduce differential primitive assembly (DPA) into NeRF to output a 3D occupancy field in place of density prediction, where the predicted occupancies serve as opacity values for volume rendering. Our network, coined DPA-Net, produces a union of convexes, each as an intersection of convex quadric primitives, to approximate the target 3D object, subject to an abstraction loss and a masking loss, both defined in the image space upon volume rendering. With test-time adaptation and additional sampling and loss designs aimed at improving the accuracy and compactness of the obtained assemblies, our method demonstrates superior performance over state-of-the-art alternatives for 3D primitive abstraction from sparse views.